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2*(cos^3(x))−(cos^2(x))+2*cos(x)−1=0. la ecuación

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Solución numérica:

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Solución

Ha introducido [src]
     3         2                      
2*cos (x) - cos (x) + 2*cos(x) - 1 = 0
$$\left(\left(2 \cos^{3}{\left(x \right)} - \cos^{2}{\left(x \right)}\right) + 2 \cos{\left(x \right)}\right) - 1 = 0$$
Gráfica
Respuesta rápida [src]
     pi
x1 = --
     3 
$$x_{1} = \frac{\pi}{3}$$
     5*pi
x2 = ----
      3  
$$x_{2} = \frac{5 \pi}{3}$$
     pi        /      ___\
x3 = -- - I*log\1 + \/ 2 /
     2                    
$$x_{3} = \frac{\pi}{2} - i \log{\left(1 + \sqrt{2} \right)}$$
     pi        /      ___\
x4 = -- + I*log\1 + \/ 2 /
     2                    
$$x_{4} = \frac{\pi}{2} + i \log{\left(1 + \sqrt{2} \right)}$$
     3*pi        /      ___\
x5 = ---- - I*log\1 + \/ 2 /
      2                     
$$x_{5} = \frac{3 \pi}{2} - i \log{\left(1 + \sqrt{2} \right)}$$
     3*pi        /      ___\
x6 = ---- + I*log\1 + \/ 2 /
      2                     
$$x_{6} = \frac{3 \pi}{2} + i \log{\left(1 + \sqrt{2} \right)}$$
x6 = 3*pi/2 + i*log(1 + sqrt(2))
Suma y producto de raíces [src]
suma
pi   5*pi   pi        /      ___\   pi        /      ___\   3*pi        /      ___\   3*pi        /      ___\
-- + ---- + -- - I*log\1 + \/ 2 / + -- + I*log\1 + \/ 2 / + ---- - I*log\1 + \/ 2 / + ---- + I*log\1 + \/ 2 /
3     3     2                       2                        2                         2                     
$$\left(\left(\frac{3 \pi}{2} - i \log{\left(1 + \sqrt{2} \right)}\right) + \left(\left(\left(\frac{\pi}{3} + \frac{5 \pi}{3}\right) + \left(\frac{\pi}{2} - i \log{\left(1 + \sqrt{2} \right)}\right)\right) + \left(\frac{\pi}{2} + i \log{\left(1 + \sqrt{2} \right)}\right)\right)\right) + \left(\frac{3 \pi}{2} + i \log{\left(1 + \sqrt{2} \right)}\right)$$
=
6*pi
$$6 \pi$$
producto
pi 5*pi /pi        /      ___\\ /pi        /      ___\\ /3*pi        /      ___\\ /3*pi        /      ___\\
--*----*|-- - I*log\1 + \/ 2 /|*|-- + I*log\1 + \/ 2 /|*|---- - I*log\1 + \/ 2 /|*|---- + I*log\1 + \/ 2 /|
3   3   \2                    / \2                    / \ 2                     / \ 2                     /
$$\frac{\pi}{3} \frac{5 \pi}{3} \left(\frac{\pi}{2} - i \log{\left(1 + \sqrt{2} \right)}\right) \left(\frac{\pi}{2} + i \log{\left(1 + \sqrt{2} \right)}\right) \left(\frac{3 \pi}{2} - i \log{\left(1 + \sqrt{2} \right)}\right) \left(\frac{3 \pi}{2} + i \log{\left(1 + \sqrt{2} \right)}\right)$$
=
    2 /    4         4/      ___\        2    2/      ___\\
5*pi *\9*pi  + 16*log \1 + \/ 2 / + 40*pi *log \1 + \/ 2 //
-----------------------------------------------------------
                            144                            
$$\frac{5 \pi^{2} \left(16 \log{\left(1 + \sqrt{2} \right)}^{4} + 40 \pi^{2} \log{\left(1 + \sqrt{2} \right)}^{2} + 9 \pi^{4}\right)}{144}$$
5*pi^2*(9*pi^4 + 16*log(1 + sqrt(2))^4 + 40*pi^2*log(1 + sqrt(2))^2)/144
Respuesta numérica [src]
x1 = 30.3687289847013
x2 = 70.162235930172
x3 = -86.9173967493176
x4 = 89.0117918517108
x5 = -17.8023583703422
x6 = 95.2949771588904
x7 = 82.7286065445312
x8 = 36.6519142918809
x9 = 55.5014702134197
x10 = 76.4454212373516
x11 = 7.33038285837618
x12 = 32.4631240870945
x13 = 38.7463093942741
x14 = 74.3510261349584
x15 = -51.3126800086333
x16 = -45.0294947014537
x17 = 99.4837673636768
x18 = -5.23598775598299
x19 = -42.9350995990605
x20 = -19.8967534727354
x21 = -13.6135681655558
x22 = 61.7846555205993
x23 = -30.3687289847013
x24 = 11.5191730631626
x25 = 93.2005820564972
x26 = 80.634211442138
x27 = -38.7463093942741
x28 = 57.5958653158129
x29 = -76.4454212373516
x30 = -95.2949771588904
x31 = -57.5958653158129
x32 = 24.0855436775217
x33 = 13.6135681655558
x34 = 5.23598775598299
x35 = -32.4631240870945
x36 = -63.8790506229925
x37 = -99.4837673636768
x38 = -26.1799387799149
x39 = 19.8967534727354
x40 = -70.162235930172
x41 = -93.2005820564972
x42 = -49.2182849062401
x43 = -24.0855436775217
x44 = -55.5014702134197
x45 = 17.8023583703422
x46 = 63.8790506229925
x47 = -74.3510261349584
x48 = -7.33038285837618
x49 = 49.2182849062401
x50 = -89.0117918517108
x51 = -68.0678408277789
x52 = -82.7286065445312
x53 = 1.0471975511966
x54 = 51.3126800086333
x55 = -61.7846555205993
x56 = -36.6519142918809
x57 = -80.634211442138
x58 = -1.0471975511966
x59 = -11.5191730631626
x60 = 68.0678408277789
x61 = -564.439480094966
x62 = 86.9173967493176
x63 = 45.0294947014537
x64 = 26.1799387799149
x65 = 42.9350995990605
x65 = 42.9350995990605